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# Re: st: Regression discontinuity with interrupted time series

 From William Buchanan To statalist@hsphsun2.harvard.edu Subject Re: st: Regression discontinuity with interrupted time series Date Thu, 7 Mar 2013 12:46:34 -0800

```I have tried to find the paper that Joshua referenced in the initial query and had little luck.  I found another paper written by one of those authors citing the paper referenced by Joshua.  Perhaps it would be helpful if Joshua could provide a link to find the paper that he referenced so others can get a better idea of what he is trying to do?

On Mar 7, 2013, at 11:20 AM, Ariel Linden. DrPH <ariel.linden@gmail.com> wrote:

> Austin is absolutely right here. For an interesting historical perspective,
> RD and ITSA originated from the same basic idea. That is, find a continuous
> x-variable and define a cutoff. In the case of ITSA, the x-variable is
> "time" and we are interested in both the "step" (first month of the
> intervention), and the "trend" (of all the months after the start of the
> intervention). In RD, the x-variable is also continuous, but here we care
> only about the average effect determined by the local values on either side
> of the cutoff.
>
> Given this general perspective, it seems an oddity to combine the two
> methods, since they require a x-variable which is going to differ, and a
> cutoff, which is going to differ. It seems as if you'd be referring to a
> sub-group analysis in which the subgroupings were decided at one level of
> the analysis and then compared at the next level (e.g., right side of the
> cutoff on the RD analysis, then analyzed at the time cutoff on the ITSA)...
>
> It is difficult to imagine how this could be done in any valid fashion...
>
> Ariel
>
> Date: Wed, 6 Mar 2013 16:51:24 -0500
> From: Austin Nichols <austinnichols@gmail.com>
> Subject: Re: st: Regression discontinuity with interrupted time series
>
> Joshua Mitts <joshua.mitts@yale.edu>:
> You need to be a lot more clear about your scientific model of the
> data generating process.  I have not read the cited paper, but I am
> doubtful about the marriage of RD and ITS. The point of RD is that
> outcomes of observations on either side of the cutoff are identical on
> average except for treatment status so the jump in outcomes at the
> cutoff is the effect of treatment; that is not true if you think
> treatment has some dynamic impacts, or in other words the effect of
> treatment increases (or decreases) in the assigment variable, so that
> you do not want the instantaneous impact of treatment at the cutoff,
> but some effect away from the cutoff.  Imagine it this way: you have
> an announcement event that affects stock prices at noon but you do not
> want to compare stock prices at one minute after noon to noon because
> you think the event actually changes the time path of investment and
> you want changes in market valuation over some period until the
> announced policy change takes place.  This is no longer a good
> situation for RD if you are thinking about comparing across time. You
> can still use the dummy for above the cutoff at time t as a dummy for
> treatment in periods after t, but the comparison will not have the
> clean RD interpretation (where the counterfactual is essentially
> observed if the data is dense around the cutoff) if you are using time
> as an assignment variable. Can you assume linear trends before and
> after time t? You can define time as time minus t so that the constant
> is the jump in mean outcomes at t, and the dummy for above the cutoff
> is the instrument for treatment; if they are perfectly collinear you
> have a "sharp" design but you may want to also estimate a change in
> trend after t for the treatment group, for which you may need an
> additional instrument--the key here is how the cutoff is defined.  Is
> the variable that is compared to the cutoff subject to manipulation?
> Changing over time? Only examined at time t?  If you have an assigment
> variable that is not time, you are back in the world of RD, and you
> may be better off with a long difference in outcomes (reducing
> problems due to measurement error in fixed effect models), e.g. y at
> t+5 minus y at t-5, regressed on treatment in the usual RD manner.
>
> On Wed, Mar 6, 2013 at 11:00 AM, Joshua Mitts <joshua.mitts@yale.edu> wrote:
>> Hi,
>>
>> How can I combine regression discontinuity with interrupted time
>> series analysis in Stata?  I have repeated observations of an outcome
>> variable for ~180 units over time, an intervention at time t at a
>> cutoff value, and more repeated observations post-intervention.  With
>> ordinary RD, I can only measure the outcome individually at t+1, t+2,
>> etc.  It seems this is an active area of research[1], but I'm not sure
>> how to implement it in Stata.  Any suggestions would be greatly
>> appreciated.
>>
>> Thank you,
>> Josh
>>
>> --
>> Joshua Mitts
>> Yale Law School '13
>> joshua.mitts@yale.edu
>
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